Let \( f(n)=\left|\begin{array}{ccc}n & n+1 & n+2 \\ { }^{n} P_{n} ...
Let \( f(n)=\left|\begin{array}{ccc}n & n+1 & n+2 \\ { }^{n} P_{n} & { }^{n+1} P_{n+1} & { }^{n+2} P_{n+2} \\ { }^{n} C_{n} & { }^{n+1} C_{n+1} & { }^{n+2} C_{n+2}\end{array}\right|, w \)
P
where the symbols have their usual meanings. The \( f(n) \) is divisible by
(a) \( n^{2}+n+1 \)
(b) \( (n+1) ! \)
(c) \( n ! \)
(d) none of these
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